# st: Cumulative probabilities

 From Evans Jadotte To statalist@hsphsun2.harvard.edu Subject st: Cumulative probabilities Date Tue, 20 Oct 2009 16:56:31 +0200

```Hello listers,

```
This is not a Stata question but I hope somebody can give me a hint on this statistical issue.
```
I am estimating cumulative probabilities of the following function:

y/ijk/ = b0 +b1/x//ijk/ + e/ijk/ + u/.jk/ + u../k

/

```
where u/.jk/ and u../k /are two random intercepts with variance Sigma^2 (u/.jk/) and Sigma^2 (u/..k/). The variance of my raw residuals is Sigma^2 (e/ijk/)//). The cumulative probabilities I want to calculate are of the form:
```
Phi((z-xb-uhat/.jk/ - uhat../k/)/sqrt(?))

```
where Phi denotes the standard normal cumulative density. My question is: should the square root, sqrt, in the denominator contain just the variance of the raw residuals, i.e. Sigma^2 (e/ijk/)//, as some books suggest? Or should it bear, according to my logic, the total variance of the model, which would be the sum Sigma(e^2 /ijk/) + Sigma^2 (u/.jk/) + Sigma^2 (u/..k/)?
```